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Quantile regression and variable selection for the single-index model

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  • Yazhao Lv
  • Riquan Zhang
  • Weihua Zhao
  • Jicai Liu

Abstract

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.

Suggested Citation

  • Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:7:p:1565-1577
    DOI: 10.1080/02664763.2014.881786
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    References listed on IDEAS

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    Cited by:

    1. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
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    3. Huilan Liu & Hu Yang & Changgen Peng, 2019. "Weighted composite quantile regression for single index model with missing covariates at random," Computational Statistics, Springer, vol. 34(4), pages 1711-1740, December.
    4. Xu, Qifa & Zhou, Yingying & Jiang, Cuixia & Yu, Keming & Niu, Xufeng, 2016. "A large CVaR-based portfolio selection model with weight constraints," Economic Modelling, Elsevier, vol. 59(C), pages 436-447.

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